In the past decades, dimensionality reduction has been an active research area. Dimensionality reduction techniques transform high-dimensional data into a meaningful representation of reduced dimensionality, ideally close to its intrinsic dimensions [1]}. The intrinsic dimensions of data are the minimum features needed to account for the observed properties of the data [2]}. High-dimensional data typically involves a significant amount of noises that can easily mislead to wrong conclusions, and analyzing high-dimensional data is often computationally intractable. For this reason, applying dimensionality reduction techniques is common in many applications involving a large number of variables, including digital photographs, speech recognition, and bioinformatics [1]}.
